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## Half-life of knowledge

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**Half-life of knowledge**Hari V Sahasrabuddhe Kanwal Rekhi School of I.T., IITB hvs@it.iitb.ac.in**what is half-life?**Definition: The time required for the quantity of a chemical, drug or radioisotope to fall to half. For example, if the quantity now is 32, and half-life is 10 days, the quantity will be 16 after 10 days, 8 after 10 more days, etc.**First used “Half-life of knowledge”**Fritz Machlup (1902-83)**Does knowledge decay like that?**No, but it may become useless when the situation changes**A progression of terms**• Data: factual information, often numeric • Information: specific knowledge • Knowledge: familiarity, awareness, understanding • Wisdom: insight, ability to judge Our use of “knowledge” is a bit fuzzy – it fits somewhere in this progression.**What is new in Oracle9i?**• Oracle Streams (replace Oracle Advance Replication and Standby Databases) • Cluster file system for Windows and Linux (raw devices are no longer required) • (etc.)**MySQL: Changes in 5.0.2**Warning: Incompatible change!NOT a BETWEEN b AND c is parsed as NOT (a BETWEEN b AND c) rather than as (NOT a) BETWEEN b AND c**Even mathematics!**Is mathematics necessary? Moving Beyond Myths, published by the National Academy of Sciences, says so, but Prof. Dudley of DePauw University does not agree! (See references)**Halting problem - definition**Given a description of an algorithm and its initial input, determine whether the algorithm, when executed on this input, ever halts (completes). The alternative is that it runs forever without halting.**Halting problem - answer**Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible inputs cannot exist. We say that the halting problem is undecidable.**Halting problem – informal proof**• Let P be a program that reads any program Q and prints 1 if Q halts, 0 if not. • Define P’: • read program Q • simulate P on input Q • if output of step 2 is = 1, go to step 2 • Halt • What happens when P’ is fed to P’?**Halting problem – formal proof**Turing’s formal proof is based on Turing Machine, a model of computation with a finite controller coupled to a unbounded memory**Another model of computation**-calculus • Allows us to define a recursive function • Foundation for LISP class of programming languages**Decidable but hard problems**• Hamiltonian circuit: a circuit that visits all vertices of a given graph • We don’t know how to find one in any arbitrary graph in time limited by a polynomial, any polynomial, of the number of vertices. • If you can solve that one, a number of other problems are solved!**Hard - example**• Remember Cramer’s rule? n*n determinant => n (n-1)*(n-1) determinants • Time for n*n determinant equals roughly n*time for an (n-1)*(n-1) determinant • A PC which can calculate a 2*2 determinant in 0.5*10-9 seconds needs almost 1 year to calculate a 19*19 determinant by Cramer’s rule, and 19 years for a 20*20 determinant!**Hard example contd.**• We could use a supercomputer. A 60 teraflop supercomputer can calculate a 19*19 determinant in less than 17 hours (but even it will need about 18 years for a 22*22 determinant) • So, faster computers do not compensate for algorithmic complexity**First programmer**Charles Babbage described his analytical engine in 1834, and in 1842-43 Lady Lovelace either created or corrected a program for it to computeBernoulli numbers(first defined in print in 1713) (The analytical enginecould never actually be built.)**How many programming languages are there?**• Thousands of them! • Main types • Imperative (c, c++, java, …) • Functional (LISP, SCHEME) and applicative (APL) • Declarative (PROLOG)**BCS: Future challenges**Conference: Brit. Comp. Soc., 29-31 March 2004 • Two separate reports, on “Grand Challenges” in education and research • Either report identifies seven challenges • Most challenges arisefrom spread of computing to new areas, e.g. embedded systems, memories for life**Identifying lasting knowledge**• Abstract rather than concrete • Technology-independent areas, e.g. maths, theoretical CS, architecture, … • Older, still useful knowledge • (if it survived n years it might survive n more years)**What after you graduate?**• Self-study and reference skills • library, bookstores, search engines, … • List of references is available • These were gathered using web search